I found that some highly shock sensitive explosives like lead azide, mercury fulminate have a relatively high auto-ignition temperature. I want to know if it's a general property or not and why so? Doesn't shock sensitivity means that the molecular bonds can be broken easily by supplying only a small amount of energy?
Yes -- but only to a degree
I assume you are talking primarily about explosives. All explosives are sensitive to both shock and heat to some degree. They are also sensitive to friction and spark. In most jurisdictions, as part of the regulatory approval process for new explosives the initiation sensitivity to each of these stimuli is determined with standardised tests.
In general, the lower the activation energy of the decomposition reaction, the greater the sensitivity to all stimuli. However, there is no simple relationship between sensitivity to different stimuli. Comparing two explosives, one may be more sensitive to impact than the other, but less sensitive to heat; a third may be less sensitive to either heat or impact, yet very sensitive to friction.
These sensitivities are not only a function of the chemical nature of the explosive, but also its physical form, purity, and the other ingredients in a composition. For example – not surprisingly! – addition of oily or greasy ingredients, even in small amounts, tends to reduce friction sensitivity. Most famously, liquid nitroglycerine is extremely shock sensitive, but is greatly desensitised by adsorption into a porous medium.
Again, for some important crystalline primary explosives the heat sensitivity is more or less fixed, but the shock sensitivity depends on the particle size distribution.
Shock and heat sensitivity are only weakly related
The shock sensitivity of an explosive is the degree to which a physical shock can set off an explosion in the compound. The heat sensitivity is the equivalent for heat. Both of these properties depend not just on the chemistry of the explosive but also its physical form and the device that contains it. This is because the physics of an explosion depends on how fast shock waves propagate in the substance. Whether heat alone triggers an explosion depends on whether heat can initiate a shockwave.
There are some explosives that are exquisitely sensitive to shock like nitroglycerine as a liquid. But even liquid nitroglycerine can be burned without triggering an explosion (not, to be sure, an experiment I'd recommend as a class demonstration).
Useful explosives should not be either too heat or shock sensitive or they will be impractical in real world uses. Many usable explosives are not very heat sensitive as a matter of design. For example, TNT can be melted by steam making it easy to fill munitions. C4 plastic explosive can be set on fire without risking an explosion (and was widely used as a source of cooking heat in Vietnam).
And excess shock sensitivity is also undesirable in useable explosives which is why Nobel made so much money from finding a way to tame nitroglycerin by absorbing it in clay. Modern explosives need fairly strong shocks to set them off so the accidental explosions are minimised.
The lack of a simple relationship between thermal and shock sensitivity is an indication that explosive properties are more complex than just having a compound where some bonds are easy to break. The difference between something that burns easily and an explosive involves not just the bonds but whether a physical shock wave can propagate through the material with enough energy to break more bonds. Heat alone will often not initiate such a wave, which is why many explosives can be safely burned.